The answer is the ddns-updates off;. It tells dhcpd to not send a DNS update for this host.

I found this answer by reading, yes, reading, the man page. Here is the extract from man 5 dhcpd.conf:

The ddns-updates statement
ddns-updates flag;
The ddns-updates parameter controls whether or not the server will
attempt to do a DNS update when a lease is confirmed. Set this to
off if the server should not attempt to do updates within a certain
scope. The ddns-updates parameter is on by default. To disable DNS
updates in all scopes, it is preferable to use the ddns-updates-style
statement, setting the style to none.